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2 results

  • Weak convergence of the extremes of branching Lévy processes with regularly varying tails

  • Part of
  • Yan-xia Ren, Renming Song, Rui Zhang
  • Journal:
    Journal of Applied Probability / Volume 61 / Issue 2 / June 2024
    Published online by Cambridge University Press:
    06 December 2023, pp. 622-643
    Print publication:
    June 2024
    • Article
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  • We study the weak convergence of the extremes of supercritical branching Lévy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, $\mathbb{X}_t$ converges weakly. As a consequence, we obtain a limit theorem for the order statistics of $\mathbb{X}_t$.